$J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 2x + 7$ and $ JT = 4x + 1$ Find $CT$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {2x + 7} = {4x + 1}$ Solve for $x$ $ -2x = -6$ $ x = 3$ Substitute $3$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 2({3}) + 7$ $ JT = 4({3}) + 1$ $ CJ = 6 + 7$ $ JT = 12 + 1$ $ CJ = 13$ $ JT = 13$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {13} + {13}$ $ CT = 26$